Inverse Cosine (ACOS) Calculator
Enter a value for x in the range -1 to 1 to compute acos(x). Results are shown in both radians and degrees.
What Is ACOS?
In trigonometry, acos means the inverse cosine function, also called arccos. It answers this question:
“What angle has a cosine equal to x?”
So if you type x = 0.5, acos returns the angle whose cosine is 0.5. That angle is 1.0472 radians or 60°.
ACOS Formula and Range
Definition
If y = acos(x), then cos(y) = x.
Important limits
- Domain of x: from -1 to 1 (inclusive)
- Range of acos(x): from 0 to π radians
- Equivalent degree range: 0° to 180°
If your input is outside -1 to 1, real-valued acos is undefined, and a standard calculator should show an error.
How to Use This ACOS Calculator
- Type a number between -1 and 1 in the input box.
- Optionally use the slider for quick values.
- Select decimal precision.
- Click Calculate ACOS to get radians and degrees.
You can also press Enter while focused on the input field.
Common ACOS Values
acos(1) = 0radians = 0°acos(0.5) = π/3radians ≈ 60°acos(0) = π/2radians = 90°acos(-0.5) = 2π/3radians ≈ 120°acos(-1) = πradians = 180°
Where Inverse Cosine Is Used
Physics and engineering
ACOS appears in vector math when finding the angle between two vectors using the dot product formula.
Computer graphics and robotics
When converting directional data to angles, inverse trigonometric functions are essential for orientation and control.
Surveying and navigation
ACOS helps convert measured ratios into meaningful angular directions.
ACOS vs ACoS (Advertising)
People sometimes search “acos calculator” when they mean Amazon ad metric ACoS (Advertising Cost of Sales). That is different from math acos:
- acos (math): inverse cosine function
- ACoS (marketing): ad spend ÷ ad revenue × 100%
This page is specifically for the mathematical acos function.
Tips to Avoid Mistakes
- Always check that input is between -1 and 1.
- Know whether your class or software expects radians or degrees.
- Round only at the final step when possible.
- Use enough decimal precision for technical work.
Quick FAQ
Why am I getting an error?
Most likely your input is outside the valid domain (-1 to 1) or is not a number.
Is acos the same as 1/cos?
No. acos(x) is inverse cosine; 1/cos(x) is secant.
Does this calculator support radians and degrees?
Yes. It outputs both units at once for convenience.